Journal article
On extensions of rational modules
Israel Journal of Mathematics, Vol.199(2), pp.585-622
03/2014
DOI: 10.1007/s11856-013-0070-3
Abstract
Given a topological algebra A, we investigate when the categories of all rational A-modules and of finite-dimensional rational modules are closed under extensions inside the category of A-modules. We give a complete characterization of these two properties, in terms of a topological and a homological condition, for complete algebras. We also give connections to other important notions in coalgebra theory such as coreflexive coalgebras. In particular, we are able to generalize many previously known partial results and answer some questions in this direction, and obtain large classes of coalgebras for which rational modules are closed under extensions as well as various examples where this is not true.
Details
- Title: Subtitle
- On extensions of rational modules
- Creators
- Miodrag Iovanov - Depatrment of mathematics University of Iowa 14 MacLean Hall Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Israel Journal of Mathematics, Vol.199(2), pp.585-622
- DOI
- 10.1007/s11856-013-0070-3
- ISSN
- 0021-2172
- eISSN
- 1565-8511
- Publisher
- The Hebrew University Magnes Press; Heidelberg
- Language
- English
- Date published
- 03/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985821802771
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